Design Optimization of Active Magnetic Thrust Bearing ...

Multi-Objective Genetic Algorithms
A Thesis submitted
for the Degree of
Guwahati
TH-832_04610307
CERTIFICATE
It is certified that the work contained in this thesis entitled Design
Optimization of Active Magnetic Thrust Bearing Systems Using Multi-
Objective Genetic Algorithms by Mr. Jagu Srinivasa Rao (Roll no.
04610307) has been carried out under my supervision and that the work
has not been submitted elsewhere for a degree.
Dr. Rajiv Tiwari Professor
Department of Mechanical Engineering
Guwahati - 781 039, INDIA
and rose again on the third day
TH-832_04610307
TH-832_04610307
Acknowledgements
I am deeply indebted to my supervisor Prof. Rajiv Tiwari for his perseverance and never
quitting attitude who tolerated with me all these years, supported and allowed me to shape
up into what is important (a character). His integrity, humbleness and learning nature is a
model to follow. I am thankful to him for introducing me to an exciting multi disciplinary
and emerging area of research. His enduring, practical and friendly guidance in the research
helped me move forward in understanding the subject as well as the surroundings in depth. I
am also thankful to the other members of my doctoral committee, Prof. Santosha Kumar
Dwivedy, Prof. Debabrata Chakraborty, and Dr. Harshal B. Nemade for their rational and
insightful suggestions, comments, discussions, and corrections which helped me to enhance
my research into connecting areas. I am also thankful to Prof. C. Sujatha (IIT Madras) for
her rational evaluation.
I would like to thank all the faculty of the department of Mechanical Engineering
(especially Dr. K. S. R. K. Murthy, Prof. Anoop Kumar Das, and Dr. U. K. Saha) who were
always ready to help by giving valuable suggestions which boosted my confidence in
pursuing the research. I am also thankful to Mr. Dhruba Jyoti Bordoloi for his assistance in
vibration laboratory and Mr. Amal Kalita for his assistance in CAD laboratory. I am
thankful to the faculty and staff of computer centre, library, student affairs, academic affairs,
research and development, establishment and other administrative departments of the
institute who are directly or indirectly involved in completion of my research.
My special thanks go to Mr. Sachin Kumar Singh (my successor from M Tech) and Mr.
A. V. Dhanunjaya Reddy (M. Tech-2 nd
year) whose mutual sharing with me is a blessed
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Acknowledgements viii
time of learning. I am also thankful to all of my other friends, colleagues, juniors, and
seniors with whom I spent heartfelt moments and learned lot in practical life.
I am deeply indebted to my parents whose constant love and prayers are a blessing. I am
also thankful to my siblings and in-laws for their well-wishes and support during this
research. Finally I am thankful to my wife, Lokeswari who is a source of encouragement,
enduring the gap of distance and time between us without whose love, cooperation and
prayers I would not be able to come to this end. I am also thankful to my church members
for their prayers about my research.
Last but most importantly, if there was nothing eternal there would be nothing temporary.
If there is no permanent source of intelligence, knowledge, wisdom, character and capability,
there would be no such quality seen in the world. Science is the study of character and
creativity of God, and engineering is the imitation of the work of His hands. I am in
adoration of my Lord who is praise worthy for all His power and knowledge and wisdom
poured in this universe. He is the source of all character. He came down to earth, died on the
cross for my sin and rose again from the dead with a promise that he will rise whoever
believes him as the genuine one. He is my strength in doing great things and enduring
hardships of life.
Jagu Srinivasa Rao
TH-832_04610307
Abstract
In the present work, an optimum design and analyses of active magnetic thrust bearings
(AMTB) and hybrid magnetic thrust bearings (HMTB) have been carried out. The active
magnetic bearing contains only electromagnets, whereas, the hybrid contains both the
electro-magnets and permanent magnets. Initially, the optimization has been carried out
using single-objective genetic algorithms (SOGA). Two objectives, namely the power-loss
and overall weight of the bearing, are considered one at a time. Different constraints
considered are the maximum current density flow in the coil, the maximum flux density
flow in the stator iron, the maximum power-loss allowed, and the maximum space occupied
by the bearing. Two objectives considered are found to be conflicting. This led to the
attempt of optimization by using multi-objective genetic algorithms (MOGA) by
considering two objectives simultaneously namely, the power-loss and overall weight of the
bearing. The effect of load on the Pareto frontier has been studied, and the load is found out
to be an objective in addition to the weight and the power-loss.
A complex system of double-acting hybrid magnetic thrust bearings (DAHMTB) with a
centralized controller as an integrated system has been optimized by using MOGA. Five
objectives are considered with three for the actuator and two for the controller. Additional
constraints considered are stability conditions of the controller.
Though power amplifiers can be designed with respect to designed controller
requirements, sometimes it is not possible to have the required power amplifiers as a
standard one, and one has to design the controller by taking the constraints of the power
amplifier available at hand. Though centralization of controller requires less number of
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Abstract x
power amplifiers, but needs some complex winding scheme and control strategies. To go for
a simpler winding and control strategies one may have to go for a decentralized actuator,
controller and power amplifier in double acting magnetic bearing systems. Hence, the
design optimization methodology is extended to the DAHMTB with decentralized
controller systems by taking consideration of constraints of the power amplifier, namely the
maximum power rating, and the voltage of the power amplifier.
The overall exercise of the optimization gives rise to a novel methodology of analysis of
Pareto optimal systems called Pareto optimal design analysis by which one can predict the
behavior of different designs in the Pareto front with respect to each other. It has also lead
to a general integrated design optimization methodology by which one can optimize
magnetic bearing systems with the actuator, controller, and amplifier as an integrated
system by using the SOGA or the MOGA. The behavior of different parameters with
respect to tradeoffs has been explored in detail.
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1.1 Introduction ............................................................................................................... 3
1.3 Classification of magnetic bearings .......................................................................... 8
1.4 Advantages and applications of magnetic bearings ................................................ 16
1.5 Limitations of magnetic bearings and research areas ............................................. 20
1.6 Literature review ..................................................................................................... 25
1.6.1 Design methodologies ..................................................................................... 27
1.6.3 Magnetic thrust bearings .................................................................................. 36
1.6.4 Control system technology in magnetic bearings ............................................ 39
1.6.5 Genetic Algorithms in magnetic bearing design optimization ........................ 40
1.7 Books, conferences, and journals ............................................................................ 42
1.8 Aim and objective of the present work ................................................................... 44
1.8.1 General Challenges in the Design of AMBs .................................................... 44
1.8.2 Objectives of the Design Optimization and its Importance ............................. 46
1.9 Organization of the thesis ....................................................................................... 48
Chapter 2 Formulations of Optimization Problems of Magnetic
Bearings 53
2.2.1 Geometrical Relations ..................................................................................... 58
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Contents xii
2.3 Optimization Model for the Design of Actuators of Magnetic Bearings ................ 68
2.3.1 Objective functions of actuators ...................................................................... 71
2.3.2 The design vector of Actuators ........................................................................ 74
2.3.3 Design constraints of Actuators ....................................................................... 75
2.3.4 Influence of different parameters on objectives and constraints ..................... 84
2.4 Conclusion .............................................................................................................. 86
3.1 Introduction ............................................................................................................. 87
3.2.1 Deterministic optimization methods ................................................................ 89
3.2.2 Stochastic optimization methods ..................................................................... 92
3.2.3 Genetic algorithms as the optimization tool .................................................... 93
3.3 Details of Genetic Algorithms Implemented .......................................................... 94
3.3.1 The general description of GA procedure ....................................................... 97
3.3.2 Chromosome (Representation of a solution) ................................................... 99
3.3.3 Generating the initial population ................................................................... 100
3.3.4 Evaluation of objectives and assigning the fitness ........................................ 101
3.3.5 Ranking and sorting of the population ........................................................... 103
3.3.6 The selection operator .................................................................................... 104
3.3.7 The crossover operator .................................................................................. 106
3.3.8 The mutation operator .................................................................................... 108
3.3.9 Elitism operator ............................................................................................. 110
3.4 Conclusion ............................................................................................................ 111
Chapter 4 Design Optimization of Magnetic Thrust Bearing Actuators
Using Single Objective Genetic Algorithms 115
4.1 Introduction ........................................................................................................... 115
4.2.3 Optimized Geometries of the Bearing ........................................................... 123
4.3 Conclusions ........................................................................................................... 131
Using Multi-Objective Genetic Algorithms 133
5.1 Introduction ........................................................................................................... 133
5.3 Multi-objective optimization problem formulation for AMTB ............................ 139
5.3.1 Fundamental relations .................................................................................... 139
5.3.2 Objective Functions ....................................................................................... 142
5.3.4 Constraints ..................................................................................................... 143
5.4 Numerical simulations .......................................................................................... 148
5.4.1 Input Variables ............................................................................................... 149
5.5 Sensitivity Analysis............................................................................................... 160
5.7 Conclusions ........................................................................................................... 172
Bearings Using Multi-Objective Genetic Algorithms 173
6.1 Introduction ........................................................................................................... 173
6.2.1 Input Variables ............................................................................................... 175
6.2.3 Convergence .................................................................................................. 177
6.2.5 Scatter plots ................................................................................................... 179
6.2.7 Comparison of results of MOGAs with SOGAs ........................................... 184
6.2.8 Sensitivity analysis of the chosen optimum design ....................................... 185
6.2.9 Analysis of the final population ..................................................................... 190
6.3 Conclusions ........................................................................................................... 199
Contents xiv
Chapter 7 Effect of the Load on the Design Optimization of Magnetic
Thrust Bearings using Multi-Objective Genetic Algorithms 201
7.1 Introduction ........................................................................................................... 201
7.3 Analyses of final populations ................................................................................ 208
7.3.1 Case without bias magnets (AMTB) ............................................................. 208
7.3.2 Case with bias magnets (HMTB) .................................................................. 218
7.3.3 Design characteristic differences of HMTB and AMTB ............................... 220
7.4 Conclusions ........................................................................................................... 225
Chapter 8 Design Optimization of Double-Acting Hybrid Magnetic
Thrust Bearings with Control Integration Using Multi-Objective Genetic
Algorithms 229
8.3 Actuator relations .................................................................................................. 233
8.4 Control Relations .................................................................................................. 235
8.5.1 Objective Functions ....................................................................................... 242
8.5.3 Constraints ..................................................................................................... 245
Thrust Bearings with Controller and Power Amplifier Integration Using
Multi-Objective Genetic Algorithms 279
9.3 Power Amplifier Relations.................................................................................... 283
9.4.1 Selection of the Design Vector ...................................................................... 287
9.4.2 Constraints ..................................................................................................... 287
9.5.4 Analysis of parameters of individual actuators ............................................. 305
9.6 Conclusions ........................................................................................................... 310
10.1 Conclusions ........................................................................................................... 313
10.1.2 Overall conclusions ....................................................................................... 324
10.2 Future Scopes ........................................................................................................ 329
10.2.1 Additional objectives ..................................................................................... 329
10.2.3 Decision making ............................................................................................ 331
10.2.4 Novel algorithm ............................................................................................. 331
Figure 1.1 The working principle of AMB systems ............................................................... 7
Figure 1.2 The classification of control system technology .................................................. 24
Figure 1.3 Different areas to be considered in a design methodology .................................. 28
Figure 1.4 Levels of design methodology ............................................................................. 31
Figure 2.1 A magentic thrust bearing with integrated control electronics
supporting a 250-hp industrial motor (courtesy: Synchrony, Inc., 2009) .............. 55
Figure 2.2 A magnetic thrust bearing with 17,000 N capacity for a 12,000 rpm
turbocompressor with a 120 mm shaft. (courtesy: SKF, 2009) ............................. 55
Figure 2.3 Different configurations of radial magnetic bearings (source: world
wide web) ............................................................................................................... 55
Figure 2.4 A 3D solid model of rotor with one radial and a double acting
magnetic thrust bearings (Courtesy: S2M) ............................................................ 56
Figure 2.5 A 3D solid model of a rotor system with two radial magnetic bearings
and one double acting magnetic thrust bearing (Courtesy: Synchrony,
Inc.) ........................................................................................................................ 56
Figure 2.6 A rotor AMB system with two radial and two single acting thrust
magnetic bearings .................................................................................................. 57
Figure 2.7 A rotor-AMB system with two radial and one double acting magnetic
thrust bearings ........................................................................................................ 57
Figure 2.9 Parts of actuator of a hybrid magnetic thrust bearing .......................................... 58
Figure 2.8 Parts of the actuator of an active magnetic thrust bearing ................................... 58
Figure 2.10 The geometry of an AMTB actuator ................................................................. 59
Figure 2.11 Geometries of a HMTB actuator ........................................................................ 60
Figure 2.12 The magnetic circuit and limits of air-gap in a single acting AMTB ............... 63
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List of Figures xviii
Figure 2.13 The magnetic circuit and limits of the air-gap in a single acting
HMTB .................................................................................................................... 64
Figure 2.14 The magnetic circuit (left) AMTB configuration (right) HMTB
configuration .......................................................................................................... 64
Figure 2.15 A magnetization curve with a linear range ......................................................... 79
Figure 2.16 The flow of information for the optimization .................................................... 84
Figure 3.1 Different stationary points .................................................................................... 89
Figure 3.2 A flowchart of a genetic algorithm implimented in the present work ................ 95
Figure 3.3 representation of a binary coded solution .......................................................... 101
Figure 3.4 Multi-point crossover operator ........................................................................... 106
Figure 3.5 Mechanism of mutation of operator ................................................................... 108
Figure 4.1 The flow of information between the genetic algorithm module and
the actuator analysis module in the comuputer program ..................................... 121
Figure 4.2 A flowchart of the implementation of actuator analysis in the genetic
algorithm .............................................................................................................. 122
Figure 4.3 The convergence of the minimum powerloss at load 2025 N ............................ 124
Figure 4.4 The convergence of the minimum weight at load 2025 N ................................. 124
Figure 4.5 Optimized magnetic bearing geometries for the objective function as
the minimum weight ............................................................................................ 127
the minimum power-loss ..................................................................................... 127
Figure 5.1 Representation of the design space and the objective space of an
MOOP .................................................................................................................. 136
Figure 5.2 The dominance in the multi-objective optimization .......................................... 136
Figure 5.3 The Pareto optimal front and different objective vectors ................................... 137
Figure 5.4 Convergence graphs of power-loss and weight .................................................. 151
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List of Figures xix
Figure 5.5 (a) The Pareto front of multi-objective optimization for the initial and
final populations after 100 generations (b) A procedure to select an
optimized bearing geometry from the Pareto front .............................................. 152
(a) Minimization of overall weight (b) Minimization of power-loss (c)
Minimum normalized weighted distance of the objective functions
namely the minimization of power-loss and the minimization of weight ........... 157
Figure 5.7 Scatter plots of feasible solutions of the design variables for the initial
population and the final population after 100 generations .................................. 158
Figure 5.8 Constraint violation plots of the initial population at designed load. ................. 159
Figure 5.9 Constraint violation plots of the final population after 100 generations
at designed load. .................................................................................................. 160
Figure 5.10 The variation of different quantities in the optimized final
population at the designed load ........................................................................... 165
Figure 5.11 The variation of different quantities in the optimized final
population at the designed load. .......................................................................... 166
Figure 5.12 The variation of different quantities in the optimized final population
at the designed load. ............................................................................................. 170
Figure 5.13: The variation of different quantities in the optimized final
population at the designed load. .......................................................................... 171
Figure 6.1 Convergence of fitness functions ....................................................................... 178
Figure 6.2 The variation of weight versus power-loss for the best optimized
population and a procedure to select the optimized bearing geometry
from the best population ...................................................................................... 179
Figure 6.3: Scatter plots of feasible solutions of design variables for the initial
and final populations after 100 generations ......................................................... 180
Figure 6.4 Final actuator geometries ................................................................................ 184
Figure 6.5 The variation of different quantities versus power-loss in the final
population HMTB ................................................................................................ 191
List of Figures xx
Figure 6.6 The variation of different quantities versus power-loss in the final
population HMTB ................................................................................................ 192
at the designed load .............................................................................................. 196
at the designed load. ............................................................................................. 197
Figure 7.1 The variation of weight versus power-loss for the final populations at
different loads ...................................................................................................... 204
Figure 7.2 Variation of different quantities versus power-loss (AMTB) ............................ 209
Figure 7.3 The scatter plots of design variables in design variable space (AMTB)
............................................................................................................................. 216
Figure 7.4 Variation of different quantities versus powerloss (HMTB) ............................. 219
Figure 7.5 The scatter plots of design variables in design variable space (HMTB)
............................................................................................................................. 223
Figure 8.1 Components of magnetic thrust bearing............................................................ 232
Figure 8.2 Magnetic circuit and limits of the air-gap in a double acting magnetic
thrust bearing ....................................................................................................... 232
Figure 8.3 The flow of information among different modules of computer
program ................................................................................................................ 251
Figure 8.4 Convergence of objectives with the generation (200 population 100
generations) .......................................................................................................... 253
generations) (left) best value in the population (right) average
value of the population ........................................................................................ 254
generations) (left) optimum value in the population (right) average
value of the population ........................................................................................ 255
Figure 8.7 The Pareto optimal front two dimensional sections (100 population
1000 generations) ................................................................................................. 258
List of Figures xxi
1000 generations) ................................................................................................. 259
100 generations) ................................................................................................... 260
Figure 8.10 Scatter of design variables in the design variable space (100
population and 1000 generations) ........................................................................ 262
Figure 8.11 Scatter of design variables in the design variable space (200
population 1000 generations) ............................................................................... 263
Figure 8.12 Scatter of design variables in the design variable space .................................. 264
Figure 8.13 The optimal control responses for different cases (200 population
and 100 generations) ............................................................................................ 274
and 1000 generations) .......................................................................................... 275
and 1000 generations) .......................................................................................... 276
Figure 9.1 Sequential design of a power amplifier for a given rotor, actuator and
controller system .................................................................................................. 280
Figure 9.2 A sequential design optimization of a controller for a given rotor,
actuator and power amplifier system ................................................................... 281
Figure 9.3 An integrated design optimization of a rotor, actuator, controller and
power amplifier system ........................................................................................ 281
Figure 9.4 schematic diagram of a DAHMTB with decentralized controller and
power amplifier .................................................................................................... 283
Figure 9.5 The flow of information among different modules namely the GA,
actuator, controller and power amplifier modules of computer program ............ 289
Figure 9.6 The flow of information among different modules including the GA,
actuator, sensor, controller, and power amplifier modules of computer
program ................................................................................................................ 289
Figure 9.7 The Convergence of objectives with generation (200 population,
20000 generations) ............................................................................................... 295
Figure 9.8 The Pareto optimal front two dimensional sections (200 population 20
000 generations) ................................................................................................... 297
Figure 9.9 Scatter of design variables in the design variable space .................................... 298
Figure 9.10 Responses of the chosen design with the minimum power-loss (units
Displacement in m, velocity in m/sec, acceleration in m/sec 2 , time in
sec, J in A/mm 2 , B in T, V in V and ic in A) ........................................................ 308
Figure 9.11 Responses of the chosen design with the minimum weight (units
Displacement in m, velocity in m/sec, acceleration in m/sec 2 , time in
sec, J in A/mm 2 , B in T, V in V and ic in A) ........................................................ 308
Figure 9.12 Responses of the chosen design with the maximum load
capacity(units Displacement in m, velocity in m/sec, acceleration in
m/sec 2 , time in sec, J in A/mm
2 , B in T, V in V and ic in A) ............................... 309
Figure 9.13 Responses of the chosen design with the minimum input
performance index(units Displacement in m, velocity in m/sec,
acceleration in m/sec 2 , time in sec, J in A/mm
2 , B in T, V in V and ic in
A) ......................................................................................................................... 309
Figure 9.14 Responses of the chosen design with the minimum dynamic
performance index (units Displacement in m, velocity in m/sec,
A) ......................................................................................................................... 310
Figure 9.15 Responses of the chosen design with the minimum distant member
from the utopian point (units Displacement in m, velocity in m/sec,
A) ......................................................................................................................... 310
Table 1.2 Advantages and specific applications of magnetic bearings ................................. 19
Table 2.1 A model of constrained single objective optimization problem ............................ 69
Table 2.2 A model of the constrained multi-objective optimization problem ....................... 69
Table 2.3 Influence of different objectives in terms of costs for various
applications ............................................................................................................ 72
Table 2.4 The multi-objective optimization formulation of the magnetic thrust
bearing ................................................................................................................... 83
Table 2.5 Objective functions and constraints for the magnetic thrust bearing .................... 83
Table 2.6 The influence of different constraints on different design parameters .................. 85
Table 2.7 The influence of the design and input variables on various objective
functions ................................................................................................................. 85
Table 3.1 Input parameters to the population ...................................................................... 100
Table 4.1 Input parameters assumed for the design of the actuator of magnetic
thrust bearing ....................................................................................................... 118
Table 4.2 Bounds of the design variables chosen ................................................................ 119
Table 4.3 The GA parameters assumed for the implementation of SOGA ......................... 120
Table 4.4 Number of generations and obective best values of convergence ....................... 125
Table 4.5 Optimized actuator input, design and dependant parameters ............................. 126
Table 4.6 Optimized actuator performance parameters ....................................................... 126
Table 4.7 Comparison of configurations with same objectives (differences in the
geometry) ............................................................................................................. 128
Table 4.8 Comparison of configurations with same objectives (differences in
volumes and performacne parameters) ................................................................ 129
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List of Tables xxiv
Table 4.9 Comparison of objectives with same configurations (differences in the
geometry) ............................................................................................................. 130
Table 4.10 Comparison of objectives with same configurations (differences in
volumes and performacne parameters) ................................................................ 130
Table 5.1 GA parameters assumed for the implementation of MOGA ............................... 150
Table 5.2 Initial bounds on design variables ....................................................................... 150
Table 5.3 Bounds of the design variables ............................................................................ 153
Table 5.4 Optimized bearing geometries in the final optimized population
through the multi-objective optimization ............................................................ 155
Table 5.5 Optimized bearing geometries through single objective optimization ................ 155
Table 5.6 Sensitivity analysis of optimized bearing geometries of a chosen
design * .................................................................................................................. 162
Table 5.7 The influence of design variables on different dependant parameters ................ 162
Table 6.1 Final bearing geometries of results for different cases ....................................... 183
Table 6.2 A comparision of the MOGA and SOGA results for HMTB .............................. 185
Table 6.3 Sensitivity of optimized bearing geometries of a chosen design with
bias magnets *
(results of the present chapter) ..................................................... 188
Table 6.4 Sensitivity of optimized bearing geometries of a chosen design without
bias magnets (AMTB – MOGA, Chapter 5) ........................................................ 189
Table 6.5 Comparison of cases with and without bias magnets .......................................... 198
Table 7.1 The minimum and maximum values of the final population at different
loads (AMTB) ...................................................................................................... 206
Table 7.2 Minimum and maximum values of final population at different loads
(HMTB) ............................................................................................................... 207
Table 7.3 Quantities of different parameters at different points of Figure 7.2 and
Figure 7.3 (AMTB) .............................................................................................. 210
Table 7.4 Behavior of different variables in different load regions (AMTB) ..................... 215
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List of Tables xxv
Table 7.5 Quantities of different parameters at different points of Figure 7.4 and
Figure 7.5 (HMTB) .............................................................................................. 220
Table 7.6 Behavior of different variables in different load regions (HMTB) ..................... 222
Table 7.7 Different load zones with respect to flux density saturation for the
cases of ................................................................................................................. 224
Table 8.2 The multi-objective optimization formulation of the problem ............................ 241
Table 8.3 Objective functions and constraints of the present multi-objective
optimization problem ........................................................................................... 244
Table 8.4 Influence of design variables on various objective functions .............................. 245
Table 8.5 Input parameters assumed for the DAHMTB design .......................................... 249
Table 8.6 Initial bounds of design variables assumed for the GA ....................................... 249
Table 8.7 The GA parameters assumed for the implementation of MOGA ........................ 250
Table 8.8 Percentage of feasible solutions in the parent population with
generation ............................................................................................................. 252
Table 8.9 Optimum and mean values of the final population for different cases ................ 257
Table 8.10 Bounds on design variables in the final population for different cases ............ 266
Table 8.11 Number of solutions in the specified clustered region of the design
variable space ....................................................................................................... 266
Table 8.12 Tight limits on the design variables of the final population for the
case of population size 200 run for 1000 generations ......................................... 267
Table 8.13 Bearing geometries for different cases .............................................................. 270
Table 8.14 Parameters of upper bearing and lower bearing ................................................ 271
Table 8.15 Parameters of double acting bearing in the final populations ........................... 272
Table 8.16 Parameters of controller in the final populatons ................................................ 273
Table 9.1 Multi objective optimization problem ................................................................. 288
Table 9.2 The actuator, controller and power amplifier input parameters .......................... 290
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Table 9.4 bounds assumed on the design vector variables .................................................. 291
Table 9.5 Number of feasible solutions in the population with generation ......................... 292
Table 9.6 Analysis of convergence into feasible region ...................................................... 292
Table 9.7 The best and mean values of objective functions in final populations
for different cases ................................................................................................. 294
Table 9.8 bounds on the design variables in the final populations after specified
number of generations for different cases ............................................................ 299
Table 9.9 Values of design variables for different cases ..................................................... 300
Table 9.10 Different geometrical and control parameters of upper and lower
bearing actuators and controllers ......................................................................... 301
Table 9.11 Different electrical and magnetic parameters of actuators and power
amplifiers ............................................................................................................. 302
Table 9.12 The force and power-loss parameters of upper and lower bearing
actuators ............................................................................................................... 303
Table 9.13 Parameters of double-acting bearing actuator and controller for
different cases ...................................................................................................... 304
Table 9.14 comparison of convergence of forces for different cases with different
populations ........................................................................................................... 305
Table 9.15 Comparison of convergence of forces for different cases with
different populations ............................................................................................ 306
g A The area of the air gap at poles
m A Pole face area of permanent magnet
w A Cross sectional area of coil wire
g B Flux density
e C Equivalent damping coefficient
F Resultant force of the both the actuators at operating position
c F Controlling force
m F Force purely due to permanent magnets at operating position
xi F Force at minimum position of rotor disc
xo F Force at maximum position of rotor disc
H Magnetic field intensity
J Coil current density
e K Equivalent stiffness
i K Coil MMF loss factor
L
P Total power-loss of both the actuators at operating position
max P Maximum power-loss
cr T Critical operating temperature of the bearing
T ∞
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t h Height of bearing
tub h maximum height of bearing
i Current in the coil
b i Bias current
c i Control current
D k Derivative gain
P k Proportionality gain
i k Current stiffness
x k Displacement stiffness
0g l Operating gap
m l Thickness of bias magnets
m Mass of the rotor
n Number of turns of the coil winding
ni Magneto-motence
c p
i r Inner radius of bearing
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oub r Maximum outer radius of the bearing
s r Radius of shaft
b t The back wall thickness of the bearing
c t Thickness of the coil
i t The inner wall thickness of the bearing
o t The outer wall thickness of the bearing
s t Settling time
c x
0 x
Initial displacement
ci x Nearest position of the rotor from the bearing
co x Farthest position of the rotor from the bearing
max x
maximum displacement of the rotor that is allowed from the
operating position
s x
Settling tolerance
v Voltage supplied by the power amplifier, velocity of the rotor
0 v Initial velocity
α Iron saturation factor
c γ
m γ
s γ
η Coil packing factor
τ Sampling time
ϑ Magneto-motence
f υ
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b Bias, back-wall
c Control, coil
i Nearest position of the rotor from the bearing, inner radius
lb Lower bound
m Permanent magnet
max Maximum
min Minimum
o Farthest position of the rotor from the bearing, outer radius
ub Upper bound
Superscripts
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DAHMTB Double Acting Hybrid Magnetic Thrust Bearing
GA Genetic Algorithm
MTB Magnetic Thrust Bearing
SBX Simulated Binary Crossover
Pµ Polynomial Mutation
Chapter 1
Introduction and
Literature Survey
1.1 Introduction
A force is the factor by which the objects of the universe interact with each other starting
from a nuclear particle to a celestial object. According to quantum physics there are four
kinds of fundamental forces which cause interaction between any two particles of the
physical world. These four fundamental interactions are namely the gravity, strong nuclear
interaction, weak nuclear interaction, and electro-magnetism. The gravity is sensed by
objects of mass of any small quantity even at large distances but weakest of all interactions.
The strong nuclear interaction is that which keeps the nucleons together overcoming the
repulsion due to charges of same polarity and is the strongest of all kinds of interactions.
The weak nuclear interaction is the powerful nuclear interaction which causes nuclear decay
in radioactive elements. The electromagnetic interaction acts between charged particles. The
word strong is used for strong force since the strong interaction is the "strongest" of the four
fundamental forces; its typical field strength is 100 times the strength of the electromagnetic
force, some 10 5 times as great as that of the weak force, and about 10
39 times that of the
gravitation.
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1.1 Introduction 4
The two important facts about electricity and magnetism observed by ancient world are
loadstone (also known as magnetite) attracting iron and amber attracted small objects when
rubbed with fur. The first definite statement is by Thales of Miletus (about 585B.C.) who
said ‘loadstone attracts iron’ (Fowler, 1997). In his treatise of the year 1600 De Magnete,
the English physician William Gilbert coined the new Latin term electricus, to refer to this
property of attracting small objects after being rubbed (Baigrie, 2006). The term electricity
is derived from the Latin lectrum, which came from the Greek word λεκτρον (lektron)
for amber. The term magnet is believed to be formulated from the place called magnesia
where magnet ore (i.e., the load stone) is found plenty.
Thales in the 6th century B.C. is said by later writers to have been the first to mention the
attractive property of amber. An Indian philosopher and surgeon of the same century,
Susruta is credited with having made use of the magnet for surgical purposes (Vowles,
1932). Vowles mentions that references to the attractive properties of either amber or
loadstone or both are to be found in a number of classical Greek and Roman works, as for
example the works of Plato, Aristotle, Theophrastus, Pliny, Dioscorides, Lucretius, and
others.
For a long time electricity and magnetism were assumed to be different forces. However
while preparing for an evening lecture in 1820, Hans Christian Oersted developed an
experiment that provided surprising evidence that by switching off and on of electric current,
the conductor deflected a magnetic needle nearby. Consequently Michael Faraday showed
in 1831 that a changing magnetic field can induce a current in a circuit. Conclusively from
the works of Oersted, Faraday and others, James Clerk Maxwell predicted that a changing
electric field has an associated magnetic field and consequently he unified them as
Maxwell’s equations of electromagnetism in 1864. According to the theory of TH-832_04610307
1.1 Introduction 5
electromagnetism, when charged particles are at rest they interact by electric forces, but
when in motion the charged particles will be acted upon both by electric and magnetic
forces called electro-magnetic interaction.
Before electromagnets were invented the permanent magnets were used in different
engineering and medical applications. Susruta made use of the magnet for surgical purposes.
Navigation compass is another application of permanent magnets that the early world used
in the dark ages of history which is believed to have originated in China. There are claims
that it had been known for centuries there, and that there were "south pointing carts"
presumably with built-in compasses, thousands of years earlier. Unfortunately, in 200 B.C.
or so the emperor destroyed all books and killed the scholars, so that earlier tales wouldn’t
detract from his own greatness (Fowler, 1997). Fowler also mentions that the permanent
magnetic spheres had been used by Otto von Guericke of 17th century A. D. in his
invention of the first generator of static electricity. The conversion of electrical energy into
mechanical energy by electromagnetic means was demonstrated by the British scientist
Michael Faraday in 1821. In 1827, Hungarian Anyos Jedlik started experimenting with
electromagnetic rotating devices which he called electromagnetic self-rotors. In the years of
1831-1832 Michael Faraday discovered the operating principle of electromagnetic
generators. The Dynamo was the first electrical generator capable of delivering power for
industry. The dynamo uses electromagnetic principles to convert mechanical rotation into a
pulsing direct electric current through the use of a commutator. The first dynamo was built
by Hippolyte Pixii in 1832.
Apart from the applications to motors and generators the permanent magnets were tried
to be utilized in hovering an object without contact. However, the passive systems involving
all permanent magnets faced problems in rotor positioning and stability. This problem in TH-832_04610307
1.1 Introduction 6
practice was proved by Earnshaw in 1842, as a theorem named after him, that it is not
possible to hover a body in all six degrees of freedom in a three axis passive environment
(Earnshaw, 1842). Earnshaw’s theorem indicates the necessity of stabilizing the object by
an alternative non-passive means.
Taking the restrictions of Earnshaw’s theorem into consideration there were methods
developed by means of electro-magnetic levitation. Filatov and Maslen (2001) summarized
some of these well known methods of electromagnetic levitation of an object including
using non-superconducting diamagnetic materials, conducting objects with time varying
magnetic fields, gyroscopic torques, diamagnetism of superconducting materials and
electro-magnets with feedback control systems. Among these methods non-superconducting
diamagnetic materials are still not practically implemented due to small forces developed.
The gyroscopic torques method has very few applications such as levitron (Berry, 1996;
Romero, 2003). Conductors when put on a rotor in a permanent magnetic field develop
currents in the conductor and a repulsive force against the magnetic field in which it rotates
are under development stage (Filatov and Maslen, 2001). Superconductors have increased
applications in maglev systems and magnetic bearings with developments in cryogenics and
high temperature superconductors (Bray, 2009). However the superconductors are costly
due to generation of cryogenic temperatures in their production and maintenance. Bray
provides also the information on the properties and different applications of
superconductors. The most commercially and technically implemented method is active
magnetic levitation which needs active control systems to adjust the current to bring the
system into stable operation. In this category magnetic bearings have found ample
applications in the present industrial world (Dussaux, 1990; Kasarda, 2000). The working
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principle of active magnetic bearings, classification, advantages and applications,
limitations and research areas are provided in the following subheadings.
1.2 Basic components of an AMB
A magnetic bearing (MB) system supports a rotating element on air without any physical
contact. It suspends the rotor on air with the electrically controlled or/and permanent
magnetic forces. A simple AMB system consists of a rotor, actuator, sensor, controller, and
power amplifier (Figure 1.1). Hence, an AMB is a complex interdisciplinary product where
mechanical, electrical, electronics, control, and computer fields of engineering are involved.
The magnetic actuator coil is supplied with an electric current which converts into the
magnetic flux in the stator-iron and attracts the rotor (radially or axially) due to the
magnetic force generated. The actuator supports the rotor to be positioned at a gap from the
actuator pole called the operating air-gap.
Figure 1.1 The working principle of AMB systems
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1.3 Classification of magnetic bearings 8
There are mainly two types of loads acting on the rotor namely, the static and the
dynamic. The static load include the load due to the weight of the rotor, external static loads
on the rotor due to interconnectivity to other machine elements such as springs, preloads,
etc. Dynamic loads include the mass imbalance of the rotor due to eccentricity, external
disturbances due to base vibrations, applied load variations on the system, impact forces due
to touch down bearings, etc. A current called the bias current is supplied to cancel out the
static load acting on the rotor or a set of permanent magnets are used to support the static
load. But due to the negative stiffness owing to the magnetic force a small disturbance
would move the rotor away from the operating position. Hence, the rotor should be brought
back to the operating position by using control methods. In this regard the rotor position is
sensed by a sensor and the sensor signal is given to the controller, which sends the signal to
the power amplifier based on the difference of the sensor signal from the reference signal.
To bring back the rotor to its original position, the actuator is supplied with an additional
current demanded by the controller through the power amplifier.
1.3 Classification of magnetic bearings
MBs are classified based on many factors. There is good number of classification of MBs
available in literature. One such classification involving unification of complicated issues in
MBs has been provided by Bleuler (1992). Salajer et al. (2000) gave classification of
bearing-less motors based on different factors such as type of motor (synchronous PM,
homo-polar, synchronous reluctance, switched reluctance); Stator winding configuration (4-
pole motor & 2-pole radial force, 2-pole motor & 4-pole radial force, 2-pole motor & 4-pole
radial force, Split winding, Concentrated winding, Single phase drive, 2-phase radial force);
and mechanical structure of the rotor or motor (Slice motor, Disk type rotor, Outer rotor,
TH-832_04610307
Ring type rotor). It also provides some types of motors on test machines (Induction, PM,
reluctance), and applications (Blood pump, Computer spindle, Canned pump, Bio-pump).
On the other hand Chiba et al. (2005) provided classification of different bearing-less
motors. After observing the literature available an alternative diverse classification for
magnetic bearing systems based on different factors has been provided in this section
(refer Table 1.1). MBs can be classified according to
Control action
– Active: MBs operated by purely electrically controlled magnets are called
active magnetic bearings (AMB). These require continuous power supply
and computation of the control current.
– Passive: MBs operated by purely permanent magnets are called passive
magnetic bearings (PMB). These do not require any additional power supply.
However they need some special conditions to achieve stability (Moser et al.,
2006).
– Hybrid: AMBs that involve also permanent magnets are called hybrid
magnetic bearings (HMB) (Groom et al., 2000). These combine advantages
of both the active and passive magnetic bearings. One constraint with HMB
is that the control flux should not flow through the permanent magnet.
Different configurations were proposed to make this constraint met as
follows.
Schmidt, 2008)
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Main classification Sub-classification
Forcing action • Repulsive (Ohji et al., 2004)
• Attractive (Robertson, 2003)
• Self-sensing (Maslen, 2006)
• Radial (Park and Chung, 1998)
• Tangential (Chiba et al., 2005)
• Combined axial and radial (Imoberdorf et al., 2007)
• Combined radial and tangential(Chiba et al., 1993)
• Combined axial and tangential (Ueno and Okada, 2000)
• Combined axial, radial and tangential (Han et al., 2002)
Magnetic effect • Electro-magnetic or reluctance force (Bleuler, 1992)
• Electro-dynamic or Lorenz force (Salazar et al., 2000)
• Super-conduction or Meissner effect (Bray, 2009)
• Conductors in variable magnetic flux (Filatov and Maslen, 2001)
• Non-Meissner Diamagnetic effect (No practical application; Bleuler,
1992)
Flux path • Homo polar: flux flow radial and axial (Na, 2004)
• Hetero polar: flux flow radial and circumferential (Kim et al., 2000)
Number of poles • Two pole (Schweitzer et al., 1994)
• Three pole (Chen and Hsu, 2002)
• Four pole (Maslen, 2000)
• Six pole (Maslen, 2000)
• Eight pole (Maslen, 2000)
• Sixteen pole (Kasarda, 2000)
Number of air gaps • Single air gap (Cavarec et al., 2001)
• Teeth pole (Cavarec et al., 2001)
Number of layers • Monolithic (Moser et al., 2006)
• Layered (Moser et al., 2006)
Winding scheme • Centralized (Schweitzer et al., 1994)
• Decentralized (Fan and Lee, 1995)
Motion generated or
o Flat
o Tubular
Objective of the
• Linear bearing motors (Cavarec et al., 2001)
• Bearing-less motors (Chiba et al., 2005)
• Contactless gears (Yao et al. , 1996)
• Magnetic conveyors (Ohjia et al., 2004)
• Noncontact springs and dampers (Robertson, 2003) TH-832_04610307
Forcing action
– Repulsive: When poles of same polarity used on rotor and stator (Hussien et
al., 2005).
– Attractive: When poles of opposite polarity used on rotor and stator.
– Gyro-torque: Though Earnshaw’s theorem affirms the impossibility of
hovering an object purely by passive means, some special cases such as
levitron disobey this theorem. When the speed of the rotor is more than a
critical value, the rotor is observed to be in equilibrium even when the rotor
is under passive levitation (Xu and Kian, 2008). This lead Earnshaw’s
theorem to be extended from the static equilibrium to the dynamic
equilibrium.
Sensing action
– Sensor sensing: We need additional sensor probes to sense the position of
the rotor. Generally, active magnetic bearings are of this category.
– Self sensing: Based on Lenz’s law the change of current flow in the bearing
coil and back-emf generated due to the change of position of the rotor can be
identified directly without the use of an external sensor. This technology has
been developed to the level of commercial application. An overview of the
technology is provided by Maslen (2006)
Load action
– Axial or Thrust: To support axial loads. The thrust action can be achieved by
the radial or axial bearings
• Single acting: A single rotor disc for a single actuator.
• Double acting: A single rotor disc for two actuators on both sides of
the disc.
– Radial or Journal: Used for supporting radial forces.
• Homo polar: The magnetic flux flows through poles of the same
magnet to close the magnetic circuit, i.e. radially and axially to the
rotor disc.
• Hetero polar: The magnetic flux flows through poles of different
magnets to close the magnetic circuit, i.e. radially and
circumferentially to the rotor disc.
– Tangential or Torque: This force is used for motoring action or rotating
action. This is a simple motor. The same is also used in magnetic gears.
– Combined axial and radial loading: The loading can be a combination of
above three types of loading
• Conical bearing: used for combined loading of axial and radial
(Mohamed and Emad, 1992)
• Teeth pole bearing: radial or axial bearing are used to support both
the axial and radial displacement controls (Kim and Lee, 2006)
– Combined radial and tangential loading: This is used in bearing-less motor
with a radial bearing (Chiba et al., 2005)
– Combined axial and tangential loading: This is used in a bearing-less motor
with an axial bearing (Ueno and Okada, 2000)
– Combined axial, radial and tangential loading: This concept is used in most
of the linear systems such as MAGLEV systems and newer class of bearing-
less motors (Imoberdorf et al., 2007)
Calculation of force
– Electro-magnetic effect: This is due to the reluctance force and these results
in magnetic bearings.
– Electro-dynamic effect: This is due the Lorentz force and these are called
bearing-less motors.
however, still investigations are continuing.
• Meissner or super conducting effect: This action comes when the
magnet is working as a superconductor; an image of same polarity is
induced in the rotor which generates repulsive forces of considerable
strength. Super conductors are found increasing application in the
area of magnetic bearings, bearing-less motors as well as linear
bearing motors
Flux path: This falls under the radial magnetic bearing category
– Homo polar: Flux flows radially and axially
– Hetero polar: Flux flows radially and circumferentially
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Number of poles: The number of poles affect the winding scheme, control strategy,
linearity etc. These are mainly subclass of magnetic radial bearings of hetero polar
category.
– Two pole
– Three pole
– Four pole
– Six pole
– Eight pole
– Sixteen pole
Number of air gaps: Analogical to number of poles. Tooth pole bearings have
special advantage of generating axial force in combination with radial force. The
different sub categories have been given in Cavarec et al. (2001).
– Single air gap
– Tooth-pole
Number of layers: Analogical to number of teeth or poles. This class falls under
permanent magnet radial bearings with hall batch arrays. (Moser et al., 2006)
– Monolithic
– Layered
Winding Scheme: The winding scheme with respect to other electro magnets
determines the control system strategy.
– Centralized: The supplied control current supplied to one controller linearly
dependant on the other magnet’s control current.
– Decentralized: Magnets are independently supplied with control current.
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Motion generated or constrained (Boldea and Nasar, 1999)
– Linear: These devices use both levitation and/or propulsion (Molenaar, 2000)
• Flat
• Tubular
• Axial
• Single cone
• Double cone
• Tooth pole
(Ueno and Okada, 2000).
• Axial, radial and tangential: these are used in conical bearing-
less motors, tooth pole bearing-less motors and in bevel gear
systems.
Objective of the application: Based on the purpose of application
– Motion to be constrained: Bearings and Precision stages: used for
positioning the stage or rotor at a particular position with high precision,
indexing tables, machine tool tables, etc.
– Motion to be generated in one direction while controlled in other directions:
Bearing-less motors and linear bearing motors: Motion in one axis and
TH-832_04610307
1.4 Advantages and applications of magnetic bearings 16
control in other axes. These are used for rotary drives such as transportation
systems like magnetic trains, elevators, IU-modules etc.
– Motion to be transmitted: Magnetic gears and conveyers to control the
transmission of torque.
– Energy to be absorbed: Magnetic springs and dampers: To absorb/dissipate
energy.
A number of configurations of magnetic bearing systems can be developed by combining
different kinds of the above bearing classifications.
1.4 Advantages and applications of magnetic
bearings
Any technology exists due to its advantages to certain applications. Hence, these advantages
can be tracked out from where it is applied. In this section some of the advantages of
magnetic bearings mentioned in literature have been summarized along with their
applications.
Kimura and Nigshi (1990) applied magnetic bearings in a vacuum chamber where a gear
train for the speed reduction is used in the production of Titanium powder. The different
advantages mentioned are (i) AMBs can be applied in vacuum without any problem of
lubrication pressure and vapours generation, (ii) oil free and no contamination, (iii) increase
of natural frequency due to double end free axis, (iv) increase allowable unbalance due to
non-contact support, and (v) rotation of the rotor around the principle axis of inertia by
automatically balancing the system. The above advantages also led Ota et al., (1990) of
Seiko Seiki Co., Ltd., of Japan to implement Maglev systems as a semiconductor wafer TH-832_04610307
transporter, which is carried in ultra-high-vacuum chambers where the particle generators
such as ball bearings cannot be used. The goals of the process are horizontal translation, a
pick and place motion in the vertical plane and restriction of rolling of the transporter rod.
High precision is another advantage with which a magnetically suspended (MS-type)
stepping motor was developed for ulta-high vacuum environments with high-precision of
the rotor (Higuchi et al., 1990).
Magnetic bearings are implemented in the flywheel energy storage system where
energylosses should be minimal. AMB systems show very low frictional losses and
extemely long expected operating life times (Zmood et al., 1990). In magnetically levitated
supports, the stiffness and damping parameters can be varied actively during the operation;
hence it is possible to avoid different critical speeds actively during the coast-up or coast-
down of rotors. Crossing different critical speeds by active methods is another advantage for
AMBs to be implemented in high speed rotors (Zhang and Kobayashi, 2006). AMBs are
applied in machining operation for they are superior to the mechanical one in terms of high
speed, low friction, vibration damping, and diameter of the rotational axis which gives high
precision. Therefore, AMB has the advantage that the stiffness of the machine which is
attached to the tools can be high, and the high precision and stable cutting process can be
obtained for a long time. AMBs are also superior to the air bearing for the high-speed
spindle in terms of suspension stiffness, load volume, and bearing clearance. It is a
promising tool for creating the micro- and nano-precision manufacturing (Shimada et al.,
2000).
Identification of parameters by using AMBs has applications in condition monitoring of
rotating machines. They allow for the adjustment of the damping, system monitoring and
fault detection (Lösch and Bühler, 2000). There are literature available on the fault detection TH-832_04610307
including unbalance, run out, crack on the rotor shaft etc. (Aenis and Nordmann, 1998).
Ventricular assistance devices for artificial blood pumps are being developed using the
AMB technology in biomedical engineering. Conventional rolling element bearings or ball
bearings use the processing fluid (i.e., blood) as lubricating fluid which results in damage of
blood cells and clotting problems (Song et al., 2001). As there is no lubrication needed
AMBs are effectively implemented in these devices (Wearden et al., 2006).
The interdisciplinary nature made AMBs expensive as well as posing challenging
problems in the area of control and sensing. However, it has immense power of generating
novel technologies, for example, extremely high-speed spindles, energy storage flywheels,
high precision planar moving tables, indexing tables, etc (Junga and Leeb, 2009). Due to its
highly nonlinear characteristic between the force and the current, now-a-days the AMB has
become a standard object of testing by any new control methods (Schweitzer et al., 1994).
Dussaux (1990) gave some industrial applications of AMBs in the aerospace, machine
tool, light industry and heavy industry. Kasarda (2000) discussed some advantages with
commercial applications and research applications of the magnetic bearing technology.
Okada and Nonami, (2003) gave a review of research topics in the magnetic bearing
technology based on the 8 th
International Symposium on Magnetic Bearings (ISMB-8).
Elaborated advantages and applications of the AMB technology have been explored by
Schweitzer et al. (1994), Chiba et al. (2005), and Schweitzer and Maslen (2009). Some of
the applications based on the advantages suitable to different fields of engineering are
provided in Table 1.2.
Table 1.2 Advantages and specific applications of magnetic bearings
Field of
(Kim et al., 2009).
the processing fluid.
Vacuum
technology
lubrication, and no
wagons, bases for building to absorb
earth quake vibration.
lubrication, and high speeds.
Kobayashi, 2006), system
Transportation No contact, high speed. Maglev, conveyors. (Ohjia et al.,
2004)
Precision
engineering
2005).
Aerospace Reliability, no lubrication
Turbo power No contact, no lubrication,
bearing life independent of
motors.
Material
processing
and precision.
contact free linear guides, test rig for
high speed tires.
active control.
new control methods, testing of control
methods
TH-832_04610307
1.5 Limitations of magnetic bearings and
research areas
There is theory and practice with any subject and the same is true with magnetic bearing
technology. What we expect in theory may not be reflected in practice due to assumptions
made in the development of the theory. These limitations sometimes will be stumbling
blocks for the technology to be realized into products of utility and commerce. The
objective of a research is to overcome these stumbling blocks by elimination of the
drawback or overriding through other means. Eliminating or overriding the drawback will
be resulted either by perfecting the same system or by adding another new technology into
the system. For an example a passive magnetic system cannot create a stable system. This
draw back can be overridden by using a control system which is an additional technology.
However, if this additional technology is eliminated from the system operation and if one
creates a stable system without control system then the conventional technology is perfected.
Though there are many advantages as mentioned above the magnetic bearing technology
has certain limitations which drive the further research for better solutions and applications.
Kasarda (2000) gave some limitations and research topics in magnetic bearings. Some
practical limitations of magnetic bearings were given by Schweitzer (2002). A summary of
disadvantages with some of the drawbacks of active magnetic bearing technology
mentioned in the literature and how they are overridden over years will be seen in this
section. The different issues of magnetic bearing technology lie in the areas of magnetic
materials such as permanent magnets and superconductors, control system technology,
sensing technology, and power electronics.
TH-832_04610307
1.5 Limitations of magnetic bearings and research areas 21
One of the drawbacks with passive levitation is its inability to generate static stable
equilibrium unassisted (Earnshaw, 1842). This drawback was a major stumbling block till
the active control systems were realized in 1930s (Schweitzer, 1994; Kasarda, 2000). In
1937, Beams published an article on rotating steel balls spinning in air by different methods
and finally by electromagnetic means. Holmes and Beams (1937) worked on magnetic axial
suspension systems and Kemper (1937) applied for a patent of magnetically levitated
vehicle systems, MAGLEVs.
One disadvantage with active magnetic bearings is that a continuous power supply to the
system is required to support a static continuous load. This load could be supported by a
permanent magnet to reduce the power consumption; however, the non-availability of
permanent magnetic materials which can support a moderate load within an affordable size
became a drawback. The property used for the load bearing capability within a size for
permanent magnetic materials is energy density maxBH . AlNiCo was the material known
from 1932, however, it needs large volumes. Rare earth cobalt alloys are later developed.
Later at some point of time samarium-cobalt (SmCo5) was the best permanent magnet
material which resulted in substantial increase in weight efficiency (Studer, 1977). However,
magnetic materials with higher energy density and mechanical strength Neodymium-Iron-
Boron (NdFeB) alloys are available now (Schweitzer, 1994). Working with the optimization
of the topology is another way of reduction of size (Dyck and Lowther, 1996).
The other reason of power consumption in AMB systems according to the linear control
theory is that they should work in linear range of operation. For this purpose a high bias
current should be supplied to the system at an operating position and small control currents
should be used to regulate the position of the rotor. However, virtually zero power (VZP)
TH-832_04610307
control techniques which were developed later, made it feasible to operate AMBs with all
static loads being supported by permanent magnets (Studer, 1977). Developments in
optimal control methods led to further reduction in power consumption (Maslen, et al., 1996;
Betschon and Knospe, 2001).
The power consumption also is a result of operating air-gap maintained between the rotor
disc and the electromagnet. Now nonlinear control methods further reduce the operating air-
gap to a few microns. Using complete passive magnetic levitation is another way of
eliminating the power-loss. There are cases observed where the dynamic stable equilibrium
is possible above a critical speed of rotors with the passive levitation (Berry, 1996; Xu and
Kian, 2008). Another case of passive levitation which is inherently stable in theroy during
rotation was presented by Post and Ryutov (1998) in which an array of permanent magnets
on the stator and a wire on the rotor to produce eddy currents was used.
The load bearing capacity is low in the case of AMB as compared to conventional
mechanical bearings. The specific load capacity of magnetic bearings is in the order of 40:1
which is very less when compared to conventional mechanical bearings. Different aspects of
reduction in the load capacity are the space available for the stator-iron, the saturation
magnetic-density of the stator iron, the saturation current-density of the coil, the fringing
and leakage losses, and eddy current losses. There are attempts to reduce these losses and
improve the load carrying capacity of AMB. Ferro magentic material used for the stator
with the higher saturation flux-density will increase the load carrying capacity. Efficient
usage of the space available by the stator iron and coil (Kasarda, 2000), using the stator iron
efficiently by the flux path by split flux method (Maslen, 2000), incorporating permanent
magnets into AMB (studer, 1977; sortore et al., 1990) varying the air-gap and flux path in
series and parallel (Khoo et al., 2005) are different ways of improving the specific load TH-832_04610307
capacity of AMBs. A specific load capacity of 108:1 for active systems and 450:1 for
passive systems was observed by Khoo et al. (2005).
A high investiment is involved in the procurement of control system, sensors, and power
amplifiers. Cost involved and space occupied with additional equipment in the control
system is another drawback. Now a days self sensing bearings are investigated seriously to
eliminate additional sensor probes (Maslen, 2006). Generally, equipment costs of AMBs
will be in decreasing trend. However the procurement cost of AMBs is far higher than
mechanical bearings. This requires a special analysis including maintainance, long life,
application advantage such as the semiconductor industry and biomedical appications, to
justify the cost involved (Kasarda, 2000). However, the special applications where the
conventional mechanical bearings cannot be fitted justify the cost involved in it. Gray et al.,
(1990) performed such analysis for the implementation of AMB technology in power plant
engineering.
In any dynamic system there are two issues to be dealt, the first is with internal
nonlinearities, and the second is with external uncertainties. AMBs are highly nonlinear
internally and subjected to sudden changes in loads frequently. As shown in Figure 1.2, in
control system technology these two issues are dealt with namely as the adaptive control
and the robust control, respectively. To meet these requirements control algorithms were
treated as a different part of the AMB system technology (Burrows, 1987). Initially linear
control methods were developed to make the system in dynamic stability by levitation using
high bias currents. Later the adaptive and robust methods were developed (Johnson et al.,
1998; Knospe and Tamer, 1997). Nonlinearities in magnetic bearings are very high when
they are operating at critical conditions such as near the saturation of magnetic flux density,
low bias or zero bias current operation, or very large operating air-gaps. Nonlinear control TH-832_04610307
1.5 Limitations of magnetic bearings and research areas
methods are other class of methods being used in the magnetic bearing control to deal with
these critical operating issues. Levine et al., (1996)
method for AMBs. They also provided different
with references of prior work namely the linear control including the transfer function or the
state space approach, self-tuning methods, H
modes, and fuzzy control method
Figure 1.2 The classification of control system technology
A sudden failure of some of power amplifiers or coils due to powercut or damage results
in the instability of the AMB system. The term used
tolerance and is a reliability aspect of AMBs. Fault toleran
continued operation of bearing even when some of the power amplifiers or coils suddenly
fail. The solution for this task is to gen
stable in remaining coils when some other coils fails (Na and Palazzolo, 2000). Much work
is done to make the AMB control system that will be able to generate a stable operation
(Maslen and Meeker, 1995; Na, 2004). The worst case is that the whole control system is
distablilized due to the failure of all power amplifiers and coils or due to overloading
of magnetic bearings and research areas
Levine et al., (1996) attempted a uni-mode nonlinear control
method for AMBs. They also provided different linear, adaptive and robust methods along
tuning methods, H2- method, H ∞ -method, µ-synthesis, sliding
modes, and fuzzy control methods.
The classification of control system technology
in the instability of the AMB system. The term used to deal with this problem is the fault
tolerance and is a reliability aspect of AMBs. Fault tolerant control seeks to provide
ation of bearing even when some of the power amplifiers or coils suddenly
fail. The solution for this task is to generate compensative currents that keep the system
, 2004). The worst case is that the whole control system is
24
mode nonlinear control
linear, adaptive and robust methods along
synthesis, sliding
to deal with this problem is the fault-
t control seeks to provide
ation of bearing even when some of the power amplifiers or coils suddenly
erate compensative currents that keep the system
, 2004). The worst case is that the whole control system is
TH-832_04610307
1.6 Literature review 25
beyond capability of the system. In that case mechanical bearings or permanent magnetic
bearings are used as backup bearings (Schweitzer et al., 1994; Schweitzer and Nordmann,
2009). Moreover, the rotor rests on these backup bearings when it is not rotating. These
bearing are also called as touchdown or retainer or auxiliary bearings. Using AMB as a
backup bearing is another idea being explored which would help in the fault tolerance (Cade
et al., 2009).
Till now we have described brief introduction of AMBs including the background,
working principle, classification, advantages with applications, and some drawbacks and
how they have been overcome by the years. The state of the art of different fields of AMBs
and the motivation of the present work and organization of thesis will be described in the
following section.
1.6 Literature review
The idea of letting a body hover without any contact by using magnetic forces is an old
dream of mankind. Earnshaw (1842) showed that permanent magnets alone are unable to
keep a ferromagnetic body in a free and stable hovering position in all six degrees of
freedom. In 1939, when there was already real interest in technical applications of magnetic
bearings, Braunbek gave further physical insights. Only materials with diamagnetic
properties would allow suitable configuration of permanent magnets with magnetic field
distributions for stable hovering. The diamagnetically produced magnetic forces are too
small to be of technical interest. High-temperature superconductors with diamagnetic
properties could be of high engineering value.
TH-832_04610307
1.6 Literature review 26
To make use of the large forces achievable by ferromagnets for a stable free hovering,
the magnetic field has to be adjusted continuously to the hovering state of the body. Kemper
(1937, 1938) suggested the application of this idea in transportation and physics. The first
description of a totally active magnetic suspension system was only issued in 1957 as a
French patent assigned to the Hispano-Suiza Company (Habermann and Liard, 1980). In the
middle of 1970s, a primitive electromagnet with stator windings having pole numbers of p
and (p+2) was proposed by Hermann (1973, 1974). This electromagnet was proposed as a
motor, which had a radial magnetic bearing function. A split-winding motor was proposed
by Meinke and Flachenecker (1976).
Since an electromagnet can only produce attractive force, magnetic bearings are
inherently unstable and require closed-loop control for a stable operation. The development
was limited in the early days since there was little knowledge of inverters, digital signal
processors, and field-oriented control theories at that time. A stepping motor, which was
magnetically combined with a magnetic bearing, was proposed by Higuchi (1984). Allaire
et al. (1989) presented the design of a prototype of thrust magnetic bearing for a high load-
to-weight ratio. A design method was described for magnetic devices, with the topology and
the material optimization by Dyck and Lowther (1996). Zeisberger et al. (2001) studied the
optimization of

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